Brendan Tyler was the husband of Lillian and father of Rodney. He was accidentally shot dead by Carl Gallagher in the last episode of Series 2, though as he was hit by a Police van just after it was originally thought that was what killed him. Frank quickly seized the opportunity to convince Lillian to allow him to regularly pretend to be Brendan in order to claim his benefits. Frank continued to cash Brendan's cheques years after his death and was even forced to dress similarly to him and pose as Lillian's husband to fool benefit investigators.
Brendan was in the British Navy and met Lillian on shore leave, after his death Lillian convinced Marty Fisher to put on Brendan's uniform, say the first thing Brendan ever said to her and then dance with her. Lillian tried to get Marty to then have sex with her, even offering to pay him for it but Marty panicked and escaped through her bathroom window.
Lillian mentioned in Series 3 that Brendan suffered from a stutter, having particular trouble with the letter 'S' which left him open to a lot of ridicule.
Lillian often mentions Brendan, telling little stories from their marriage, though these stories often turn out to be the plot from movies that Lillian has confused to be her own life.